Direct Observation of Magnetic Long-range Order in Ammann-Beenker Artificial Quasicrystals*

Magnetic long-range order (LRO) in 3D Ammann-Beenker tilings (ABT) has been modeled in simulations^1,2, but has yet to be experimentally observed³. We fabricated artificial ABT composed of a connected wire network of elongated Permalloy film segments that mimic classical Ising spins interacting via long-range dipolar and short-range exchange interactions. Our MC analysis of ABT (NN interactions) generated a magnetic ground state built upon distinct sublattices, similar to fivefold Penrose tilings^4,5. High-resolution images of the in-plane magnetization of ABT were acquired with scanning electron microscopy with polarization analysis (SEMPA). An annealing protocol that yielded improved agreement with the MC ground state. We developed a novel cluster covering that introduces frustration among neighboring clusters, and suggests low-energy, long-range interactions are required for full LRO, and provides a possible explanation for the non-existence of magnetic LRO in atomic quasicrystals.
1) E. Y. Vedmedenko et al., Phys. Rev. Lett. 93, (2004) 076407
2) S. Thiem, J. T. Chalker, EPL 110 (2015) 17002
3) F. Hippert, J. J. Préjean, Philos. Mag. 88 (2008) 2175
4) B. Farmer et al., Phys. Rev. B. 93 (2016) 134428
5) D. Shi et al., Nat. Phys.14 (2917) 309